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The vertical height difference between point P and point A is H = R+R * COS 45 degrees = R * [2+ (root number 2)]/2.

At (1) point P, the included angle between the velocity direction of the ball and the horizontal direction is 45 degrees, indicating that at point P, the horizontal component of the ball velocity is equal to the vertical component.

Get v y 2 = v0 2 = 2gh.

Therefore, when the ball is ejected from point A on the platform, the speed is v0 = root number (2gh) = root number {gr * [2+ (root number 2)]}

(2) The horizontal displacement of the ball in the air is set to S (that is, the horizontal distance between two points of AP)

Then s = v0 * t

And y = v0 = gt.

So s = v0 2/g = r * [2+ (root number 2)].

According to Pythagorean theorem, the distance between a and p on a circular orbit is L = root sign (H 2+S 2).

That is, l = radical number {"r * [2+ (radical number 2)]/2" 2+"r * [2+ (radical number 22)] "2} = r * [2 * [2 * (radical number 5)+ (radical number 10)]/2.